Noise-Tolerant Wireless Sensor Networks Localization via Multinorms Regularized Matrix Completion

Abstract

Accurate and sufficient location information is the prerequisite for most wireless sensor networks (WSNs) applications. Existing range-based localization approaches often suffer from incomplete and corrupted range measurements. Recently, some matrix completion-based localization approaches have been proposed, which only take into account Gaussian noise and outlier noise when modeling the range measurements. However, in some real-world applications, the inevitable structural noise usually degrades the localization accuracy and prevents the outlier recognition drastically. To address these challenges, we propose a noise-tolerant localization via multi-norms regularized matrix completion (LMRMC) approach in this paper. Leveraging the intrinsic low-rank property of euclidean distance matrix (EDM), the reconstruction problem of true underlying EDM is formulated as a multi-norms regularized matrix completion model, where the outlier noise and structural noise are explicitly sifted by $L_1$ -norm and $L_{1,2}$ -norm, respectively, while the Gaussian noise is implicitly smoothed by employing the well-known alternating direction method of multiplier optimization method. To the best of our knowledge, this is the first scheme being able to efficiently recover the unknown range measurements under the coexistence of Gaussian noise, outlier noise, and structural noise. Extensive experiments validate the superiority of our proposed LMRMC approach, outperforming the state-of-the-art localization approaches with regard to the localization accuracy. Besides, LMRMC can also achieve an accurate detection of both outlier noise and structural noise, making it promising for further nodes fault diagnosis and topology control in WSNs.